Optical correlators are employed for many optical signal processing applications, including pattern and character recognition, implementation of optical interconnections in hybrid optoelectronic parallel computers, and in artificial neural network technologies. Holographic optical correlators can compute two dimensional geometrical correlations in much less time than it takes to input an image into an optical system, to convert the output optical signal into electronic signals, and to perform electronic correlation on the resultant signals. For these reasons, they have become important elements of modern high speed optical information handling and processing systems.
Conventional optical correlators currently in use are based on discrete optical elements and free space propagation. They typically comprise two pairs of identical refractive lenses, each lens of each pair separated from its partner by a distance equal to the focal length of the lenses. A holographic filter is sandwiched between the two pairs. The first pair performs a Fourier transformation, with the input plane adjacent to the first lens of the pair and the Fourier plane adjacent to the second lens of the pair.
The complex field at the back focal plane of the first lens, which falls at the second lens because the lens spacing is equal to the focal length, provides a Fourier transformation of the input plane multiplied by a complex quadratic phase term. The second lens has an identical but opposite quadratic phase, so an exact transformation is achieved at the Fourier plane at this lens. A complex filter is placed at this plane behind the lens. The second lens pair comprising a similar pair of refractive lenses and therefore performs another exact Fourier transformation. The result at the output plane of the second lens of this second pair is the correlation function between the input signal function on the input plane of the first lens, and the filter function. In practice, the fourth lens can be omitted because the detectors generally used to sense the correlation output are sensitive only to the intensity distribution, so there is no need for phase correction.
The physical size of such correlators is large and their components must be mounted and aligned mechanically. This results in bulky set-ups, thermal instability and relatively low positioning accuracies, in the range of several microns. All of these factors makes such correlators incompatible with the small size and circuit construction techniques used in modern integrated optoelectronic technology.
Optical correlators based on variations of this classical free space model have been proposed in an attempt to obtain more compact correlators. One such correlator, as described by M. Zimmerman in "The 1992 French-Israeli Workshop on Optical Computing--Digest of Papers" edited by P. H. Cheval and I. Glaser, (Israeli Ministry of Science, Jerusalem, 1992) pp. 31-32, includes folding mirrors with lenses designed to minimise correlator dimensions.
Further miniaturisation has been obtained by the use of multiple bee's-eye lenslet arrays, as described by I. Glaser in the article "Compact lenslet-array-based holographic correlator/convolver", published in Optics Letters, Vol.20, No.14, pp.1565-1567, July. 1995. A comparison of the performance, size and speed of such correlators with that of electronic processor-based correlators and conventional folded optics correlators is shown below.
Kernel size Input size Response time Volume Correlator type (pixels) (pixels) (sec.) (cc.) Microprocessor 32 .times. 32 512 .times. 512 .about.10.sup.2 &lt;1 DSP chip 32 .times. 32 512 .times. 512 .about.1 &lt;1 Dedicated electronic 7 .times. 7 512 .times. 512 .about.10.sup.-1 .about.10 Coherent optical (folded) 64 .times. 64 64 .times. 64 .ltoreq.10.sup.-3 .about.500 Lenslet array correlator 32 .times. 32 512 .times. 512 .ltoreq.10.sup.-3 .about.20
It is evident from the above comparison that even though the lenslet array optical correlator is considerably smaller than a corresponding bulk optical correlator, it has dimensions which are still over an order of magnitude greater than those of associated optoelectronic circuit packages. There is, therefore, great need for an optical correlator which combines the speed of optical processing techniques with the small dimensions typical of microelectronic technology. In terms of the specifications in the above table, this would mean a response time of .ltoreq.10.sup.-3 sec. and a volume of &lt;1 cc., whilst maintaining high pixel count for the kernel and input image dimensions.
Planar technology is a very compact optical fabrication technology, fully compatible with microelectronic detectors and devices. In planar technology, the elements are executed on thin optical substrates, ususally as diffractive optical elements, using patterns generated by microelectronic production techniques such as photolithography and etching. Such planar optical systems have been developed to perform basic imaging functions, as described by J. Jahns and S. Walker in the article "Imaging with planar optical systems" in Optics Communications, Vol. 76, No. 5-6, May 1990, pp. 313-317.
The use of planar substrates for performing Fourier transformation has been described by S. Reinhorn, S. Gorodeisky, A. A. Friesem and Y. Amitai in the article "Fourier transformation with a planar holographic doublet" published in Optics Letters, Vol. 20, No. 5, March 1995, pp. 495-497, which is incorporated herein by reference. The article deals principally with the need to design the grating function of the holographic lens doublet used to perform Fourier transformation, in such a way as to avoid the phase errors which arise when using such lenses off-axis, as required in the planar configuration.
In the final paragraph of this article, the authors raise the possibility that optical data processing systems requiring the use of Fourier transformation, such as optical correlators and convolvers, could be constructed using planar fabrication technology. They state that "When these doublets are incorporated into optical data processing applications such as optical correlators and convolvers, the scaling factors should be taken into acount when the needed optical filters are designed." They did not however show how such a correlator could be constructed and operated.